In general, switching mixers can be used to convert an input at a first frequency into an output at a second frequency. A switching mixer that has inputs at frequencies f1 and f2 can create outputs at output frequencies that are the absolute value of the sum and difference of the input frequencies (e.g., |f1±f2|). When used to up-convert or down-convert a target input frequency to a desired output frequency, the inputs to a switching mixer are generally an input signal at a target frequency and a local oscillator at a frequency appropriate to convert the target input frequency to a desired output frequency.
Switching mixers can be used to up-convert an input signal from a lower frequency to a much higher frequency (e.g., using a local oscillator signal having a much higher frequency than the target frequency) or to down-convert an input signal from a higher frequency to a lower frequency (e.g., by using a local oscillator having a frequency that is relatively close to the frequency of the input signal).
The local oscillator signal can include a fundamental frequency and various harmonics of the fundamental frequency. For example, depending on the shape and/or duty cycle of the local oscillator signal, harmonics can be generated at the second harmonic, third harmonic, fourth harmonic, etc., of the fundamental frequency. Using a square wave with a fifty percent duty cycle as the local oscillator signal can eliminate the even harmonics of the fundamental frequency, leaving only the odd harmonics (e.g., the third, fifth, seventh, etc.).
Due to the harmonics of the local oscillator signal, signals that are not at the target frequency in the input signal can be up-converted or down-converted to the desired frequency. For example, if the target input frequency is 500 megahertz (MHz) and the desired output frequency is 10 MHz, a local oscillator with a fundamental frequency of 510 MHz can be used. If the local oscillator signal is a square wave with a 50% duty cycle, the local oscillator signal can also include the odd harmonics of the fundamental frequency at 1530 MHz, 2550 MHz, and so on. These harmonics can mix with signals at 1520 MHz, 1540 MHz, 2540 MHz, and 2560 MHz in the input signal to create signals at the desired frequency of 10 MHz. These undesired signals can create interference and/or noise by combining with the output created by mixing the signal at the target input signal with the fundamental frequency of the local oscillator.
Several approaches to limiting such undesired signals have been suggested. One such approach is using pre-conditioning circuits, such as tunable band pass or low pass filters, to eliminate signals that may combine with harmonics of the local oscillator to create undesired signals. Using such preconditioning circuitry can introduce complexity and cost into the circuit and a band pass filter can be difficult to tune for wideband applications.
Another approach that has been suggested is a classic harmonic rejection mixer which uses three alternate paths having gains of 1, √{square root over (2)}, and 1, respectively. In the classic harmonic rejection mixer, each path includes a switching mixer that mixes the input signal and the local oscillator signal. The phase of the local oscillator signal is offset in the paths with unity gain by 45 degrees and negative 45 degrees, respectively, compared to the path with a gain of √{square root over (2)}. The signals generated by the mixers on the three paths can be combined, which theoretically cancels out the components of the output signal generated by the third and fifth harmonics of the local oscillator's fundamental frequency. The advantage of the classic harmonic rejection mixer is that it cancels (or rejects) undesired signals at the desired output frequency, without requiring extensive preconditioning circuitry. However, in practice, creating an amplifier with a gain of √{square root over (2)} is difficult. Device size ratios to control the path gains can be made accurately for rational fractions, but √{square root over (2)} is an irrational number that is difficult to approximate using a rational fraction. Because of the need to approximate √{square root over (2)}, a harmonic rejection ratio (e.g., how much power of the undesired signals generated by the harmonics of the local oscillator are cancelled) achievable by the classic harmonic rejection mixer is degraded due to gain inaccuracies between the three paths.
Therefore, there is a need for new circuits and methods for performing harmonic rejection mixing.